Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃×C₁₅

Direct product G=N×Q with N=C₃² and Q=C₃×C₁₅

		d	ρ	Label	ID
C₃³×C₁₅		405		C3^3xC15	405,16

Semidirect products G=N:Q with N=C₃² and Q=C₃×C₁₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊(C₃×C₁₅) = C₁₅×He₃	φ: C₃×C₁₅/C₁₅ → C₃ ⊆ Aut C₃²	135		C3^2:(C3xC15)	405,12

Non-split extensions G=N.Q with N=C₃² and Q=C₃×C₁₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².₁(C₃×C₁₅) = C₅×C₃≀C₃	φ: C₃×C₁₅/C₁₅ → C₃ ⊆ Aut C₃²	45	3	C3^2.1(C3xC15)	405,7
C₃².₂(C₃×C₁₅) = C₅×He₃.C₃	φ: C₃×C₁₅/C₁₅ → C₃ ⊆ Aut C₃²	135	3	C3^2.2(C3xC15)	405,8
C₃².₃(C₃×C₁₅) = C₅×He₃⋊C₃	φ: C₃×C₁₅/C₁₅ → C₃ ⊆ Aut C₃²	135	3	C3^2.3(C3xC15)	405,9
C₃².₄(C₃×C₁₅) = C₅×C₃.He₃	φ: C₃×C₁₅/C₁₅ → C₃ ⊆ Aut C₃²	135	3	C3^2.4(C3xC15)	405,10
C₃².₅(C₃×C₁₅) = C₁₅×3_-¹⁺²	φ: C₃×C₁₅/C₁₅ → C₃ ⊆ Aut C₃²	135		C3^2.5(C3xC15)	405,13
C₃².₆(C₃×C₁₅) = C₅×C₉○He₃	φ: C₃×C₁₅/C₁₅ → C₃ ⊆ Aut C₃²	135	3	C3^2.6(C3xC15)	405,14
C₃².₇(C₃×C₁₅) = C₅×C₃²⋊C₉	central extension (φ=1)	135		C3^2.7(C3xC15)	405,3
C₃².₈(C₃×C₁₅) = C₅×C₉⋊C₉	central extension (φ=1)	405		C3^2.8(C3xC15)	405,4

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁